Question

If the function y=sin(f(x)) is monotonic for all values of x (where f(x)is continuous), then the maximum value of the difference between the maximum and minimum value of f(x) is

• A. $\pi$
• B. $2\pi$
• C. $\frac{\pi }{2}$
• D. $Noneofthese$

Answer 1

The correct option is A $\pi$

y = sin (f(x)) is monotoic for
$f\left(x\right)\in [2n\pi -\frac{\pi }{2},2n\pi +\frac{\pi }{2}]$or $[2n\pi +\frac{\pi }{2},2n\pi +\frac{3\pi }{2}]$